A pointwise differential inequality and second-order regularity for nonlinear elliptic systems (Q2160198)

This is a very nice paper, where the authors establish a sharp pointwise differential inequality for vectorial second-order partial differential operators, with Uhlenbeck structure. Using this, they derive optimal second order regularity properties of solutions to nonlinear elliptic systems in domains in $\mathbb{R}^n$. In the special case of $p$-Laplacian systems, their reqularity results apply for every $p > \frac32$. This extends the range of the admissible values of the exponent $p$ previously known which was for $p > 2(2-\sqrt{2}) \approx 1.1715$.